Marco Damele’s Blog

Quick Post

Let G be a finite group and φ: G—>G be an automorphism that fixes more than half of the elements of G. Prove that φ is the identity of G.

Sep 5, 2024

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Marco Damele

in Un pò di matematica
Let G be a finite non-abelian group. Show that |Z(G)| ≤ |G|/4

Sep 5, 2024

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Marco Damele

in Un pò di matematica
Is there an infinite group with a finite number of subgroups?

Sep 5, 2024

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Marco Damele

in Un pò di matematica
Let G be a finite group such that Aut(G)={e}. Prove that G is isomorphic to ℤ₂

Sep 5, 2024

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by

Marco Damele

in Un pò di matematica
Let G be a finite group. Is there always a finite group H such that G≅Aut(H)?

Sep 5, 2024

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by

Marco Damele

in Un pò di matematica
Solve in ℤ₅ the equation x⁷ + x³ – x +1= 0.

Sep 5, 2024

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by

Marco Damele

in Un pò di matematica
Let G be a group such that Aut(G) is cyclic and not trivial. Then Aut(G) is finite and his order is even.

Sep 5, 2024

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Marco Damele

in Un pò di matematica
Let f ∈ ℚ[X] irreducible, then f doesn’t have multiple roots in ℂ

Sep 4, 2024

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by

Marco Damele

in Un pò di matematica
There is no non-constant f ∈ ℤ[X]: f(x) is prime for every integer x

Aug 10, 2024

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by

Marco Damele

in Un pò di matematica
π < 4 : Visual Proof

Aug 7, 2024

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by

Marco Damele

in Un pò di matematica